Hi Cup,
Mold can be an issue where there is high humidity, lack of air circulation, and darkness. Since we all give off moisture when we are sleeping, this can be an issue with any mattress but especially in areas where it is dark and air circulation is less (such as the bottom of the mattress). By the time there is obvious mold on any mattress surface, it’s almost certain that there is more where it is not so visible.
Different materials allow for different levels of air circulation. A slatted base, breathable fibers and fabrics, and more breathable types of foam can all make mold issues much less likely.
There are basically 3 broad “categories” of foam which are latex, memory foam, and polyurethane. Of these three, latex is generally the most breathable followed by polyurethane followed by memory foam. While there is a wide variety inside each category, this is generally accurate. Because sleeping hot is also related to air circulation (or lack of it), these foams also have the same general tendency to either sleep cooler or hotter (less breathability means a foam will insulate more and sleep hotter).
Yes … very much so. Post #47 here and this thread has more information but in general a foam mattress … especially latex … does best on a slatted foundation with no more than 3" gaps (preferably less) between the slats. A wire grid foundation with a supportive surface is also a good choice.
This depends to a great degree on the type of foam used in the top of a mattress as well as the ticking/quilting materials used. More breathable foams, fabrics, and fibers at or near the top of your mattress are usually the solution to this issue. There are also some foams and materials that use “phase change” ingredients that in some cases can help with heat issues and they work through convection rather than circulation and evaporation. Sleeping hot is usually more of an issue with memory foam than it is with either polyurethane foam or better yet latex. Natural fibers on top of a mattress, natural fabrics or “phase change” fabrics, and a mattress that doesn’t sink in quite as much and sleeps more “on” the mattress than “in” the mattress are all ways of reducing heat … especially for those who have this tendency anyway.
There are so many variables in what each person needs and prefers, how they sleep, body weight and shape differences, general sensitivities, and in how each person uses the same descriptions (such as soft and firm) that without a specific frame of reference and actually seeing how each person reacts to a mattress it is very difficult to know ahead of time what mattress will work well for an individual. Having said that, an “average” recommendation is possible for a given weight/height/shape/sleeping positions even though it may not be suitable for any particular individual who is not “average”. With a frame of reference from actual testing, it is much easier to help with the “direction” of any changes or adjustments that may be needed based on specific feedback. Some general guidelines which are a good place to start any testing are in this article (about the sleeping positions) and this article (about variations in height, weight, and body shape).
When you sleep in all positions … then it becomes important to choose a layering that provides pressure relief on your side (the position with the most pressure points) as well as provides alignment in your “flattest” position (stomach). Generally a comfort layer that is “perfect” for side sleeping will allow the pelvic area to sink in too deeply for stomach sleeping (leading to a swayback position and possible back issues). This is where the “art and science” of choosing a mattress and the different design options comes into play. The most reliable way to “get it right” is to find a manufacturer or outlet that is knowledgeable and familiar with how to fit a mattress to a person and can be there in person to help you make the best decision. The best online outlets are also very good at matching their mattresses to an individual based on their height, weight, and sleeping positions as well as feedback from any mattress testing they have done.
My personal preference (in terms of value) for a position adjustable base is Reverie and I purchased a Reverie Deluxe from here. This is the same manufacturer who makes the Tempurpedic adjustable bases. Other good choices that are also more widely available are the Ergomotion (which is what Serta uses) and Leggett and Platt (which makes a wide range of adjustable bases that are also high quality but generally more expensive and not usually in the same value range IMO).
If you purchase an adjustable base then a foundation isn’t needed as the mattress can go right on the base itself.
I hope this answers most of your questions and if you have more feel free to post them 
Phoenix